Square Dance Study Hints

Triangles

A "triangle" is a three-person formation. In current usage of the term, there are two basic types, referred to as "wave-based triangles" and "tandem-based triangles".

Since a full square consists of eight dancers, the caller will typically be addressing triangle calls to two groups of three dancers – a total of six dancers – while two other dancers will not be involved.

In addition, many eight-dancer formations contain more than one pair of triangles. So the first task of the caller is to make clear which pairs are to do the call (which also tells the dancers which two dancers are not involved) – and the first task of the dancers is to understand this. The process of identifying the triangles, and the terminology used in doing that, is referred to as "triangle identification".

Once dancers understand if they are in one of the relevant triangles, their remaining task is to do the action of the call. At C-1, the call will almost always be a circulate (i.e., Triangle Circulate). There are other calls relating to triangles that are introduced in later programs, and a few other simple things that can be done with triangles in the same way as other subformations (e.g., Counter Rotate, Substitute), but mostly what you need to learn to do, with triangles as such, is how to circulate in them.

Triangle Circulates

So let's review first the important points about circulating in the two basic types of triangles.

General Rule: On a triangle circulate, each dancer moves to the next spot, based on his/her own current facing direction. Note that for all three dancers to be able to do this, without trying to occupy the same spot, they must all be moving around the triangle in the same direction – clockwise or counterclockwise. Another way of saying this is that they all have the same shoulder toward the center of the triangle. (Such triangles can therefore, in the same way as with boxes and diamonds, be referred to as "left-handed triangles" or "right-handed triangles".) There can be triangles for which this is not the case, but if the caller is going to ask you to circulate in a triangle it will almost always be one where everybody has the same shoulder into the center.

Wave-Based Triangles

A wave-based triangle consists of two dancers standing side by side, forming the "base" of the triangle, and a third "apex" dancer facing 90 degrees to them. Their spacing and position is basically the same as three of the dancers in an ordinary diamond (i.e., ignoring one of the spots in the diamond):

One shoulder of the apex dancer is facing directly at the center point between the two base dancers – in the same way as a point of a diamond has one shoulder toward the hand-hold between the two center dancers. This also means that the apex dancer is exactly the same distance from each of the two base dancers. (If you imagine the geometric shape consisting of lines connecting each pair of dancers, and you remember the terminology used in your high school geometry class, another way of saying this is that the shape is an isosceles triangle.)

On a triangle circulate in the case of a wave-based triangle, as each dancer moves to the next spot he or she adopts an appropriate facing direction so that the triangle will still be a wave-based triangle, while keeping the same shoulder toward the center.

Considering each of the three segments of this circulate path separately:

Note: If the base consists of two dancers standing side by side and facing the same way (i.e., a couple), the triangle is still referred to as "wave-based". In such a triangle the dancers would not normally be asked to do an ordinary Triangle Circulate, but the term "wave-based triangle" is still useful to be able to identify the group of three dancers and ask them to do something else.

Tandem-Based Triangles

In a tandem-based triangle, rather than the two base dancers standing side to side, they will be in tandem. The apex dancer is off to one side of the tandem, but still with one shoulder directly facing the center point between the two base dancers. Note that this means that all three dancers will be facing the same type of wall – heads or sides.

As with wave-based triangles, the general rule is that each dancer moves to the next spot while keeping the same shoulder toward the center, and for all three dancers to do this without trying to occupy the same spot they all must have the same shoulder toward the center. And when doing a circulate in a tandem-based triangle, each dancer must adopt an appropriate facing direction so that the triangle will still be tandem-based.

Considering each of the three segments of the circulate path separately:

Note that two of the segments involve turning 180 degrees, and that the apex dancer must do this while also moving forward, with respect to his/her original facing direction. A common mistake is for this dancer to move to the correct spot but forget to turn around (i.e., just slide diagonally into that base spot). A good way to avoid this mistake is to focus on the basic rule: you must keep the same shoulder toward the center of the triangle.

Note: If the base consists of two dancers facing each other or back to back, the triangle is still referred to as "tandem-based". In such a triangle the dancers would not normally be asked to do an ordinary Triangle Circulate, but the term "tandem-based triangle" is still useful to be able to identify the group of three dancers and ask them to do something else.

Terms Used in Triangle Identification

In certain formations, there may be only one pair of wave-based triangles, or one pair of tandem-based triangles, and in such cases the caller may be able to adequately identify the triangles that way, e.g., "The wave-based triangles, Triangle Circulate". But in many formations there is more than one pair of a given type, so additional terms must be used to distinguish them.

First, let's review the kinds of terms most commonly used, then we'll look at how they apply in the context of common eight-person formations.

There can be other variations, but these examples illustrate the basic approaches.

Also note that even when one kind of identification would be enough to uniquely identify the pairs, callers sometimes use more than one just to be helpful. So you might hear something like "Outside Wave-Based Triangles", even though there are no tandem-based triangles so just "Outside Triangles" would have had the same meaning.

Twin Diamonds

In the case of twin diamonds, by far the most commonly-referenced triangles will be the waved-based triangles formed by the centers of one diamond (constituting the base of the triangle) and one of the points of the same diamond (as the apex), and these are almost always identified using the "In-Point / Out-Point" terms.

There are, however, also other pairs of wave-based triangles – the ones formed by the two points of one diamond and one of the centers of the same diamond. These are almost always identified using the "Outside / Inside" terms.

Note that the "base" in these triangles is very wide, with a large gap between the two dancers making up the base. In addition, right in the middle of that gap there is a hand-hold (between the centers of the diamond). Circulating in such a triangle is therefore somewhat awkward – the centers of the diamond must release their hand-hold, one of the base dancers then has to walk a considerable distance while remembering to turn around half way, and then the new apex has to remember to join hands again with the other center of the re-formed diamond – and for this reason these triangles are much less commonly used. But they get used frequently enough that you do need to understand that they exist.

Point-to-Point Diamonds

In the case of point-to-point diamonds, the most commonly referenced triangles will be the wave-based triangles formed by the centers of one diamond (constituting the base of the triangle) and one of the points of the same diamond (as the apex). If the apexes are the very ends, these are normally identified as the "Outside Triangles"; if the apexes are the very centers, then they are the "Inside Triangles".

There are also pairs of "wide" wave-based triangles, consisting of both points and one center, but these are far less commonly used. When they are they might be identified by a term like "Out-Center Triangles".

Hourglass

In an hourglass there is just one obvious pair of wave-based triangles, and one obvious pair of tandem-based triangles.

There are actually more triangles that can be identified, for example by considering one of the very centers to form a tandem-based triangle with the far two outer (point) dancers, but additional words are needed for that, so to identify the obvious pairs normally just "the wave-based triangles" or "the tandem-based triangles" will be enough.

Galaxy

In a galaxy there is just one obvious pair of wave-based triangles, and one obvious pair of tandem-based triangles.

There are actually more triangles that can be identified, for example by considering one of the points of the outer diamond to form a wave-based triangle with the far two center dancers, but additional words are needed for that, so to identify the obvious pairs normally just "the wave-based triangles" or "the tandem-based triangles" will be enough.

Phantom Waves

In a typical "phantom waves" formation where the real dancers occupy one half of each wave, there are wave-based triangles consisting of those two dancers (as the base) and a center from one of the waves facing the other kind of wall. However, just "wave-based triangles" isn't enough to identify them, because the dancers from either pair of waves might be the base (and then a center from the other pair the apex). In this kind of situation, the triangles may be identified according to who is playing the role of base or apex. A fairly common situation is "the boy-based triangles" vs. "the girl-based triangles".

Alternatively, the caller might make use of the fact that these pairs of triangles have different handedness. So in this example "the left-handed wave-based triangles" would refer to the same pair as "the girl-based triangles".

Other Formations

There are many other formations where triangles can be found. In some cases, even though the overall formation may be unfamiliar, it's easy to see the triangles, even without any special identifying terms. For example in a "bone" formation consisting of a wave in the center and tandems on the outside along the long axis, the caller might say "the outside tandem-based triangles" to be completely clear. But because those are the obvious triangles, you might hear "the tandem-based triangles", or even just "the triangles", and it would be reasonable to assume those are the ones the caller meant.

But in other cases, the caller may need to use terms normally associated with some other formation to identify the specific triangles, even though the dancers aren't facing in a way that would normally make up such a formation. For example, if the dancers are on spots that would normally make diamonds, but the centers are facing the same kind of wall as the ends, the caller might refer to "In-Point Triangles" even though the term "point" might not otherwise be used for the ends, and even though these triangles are tandem-based (while the in-point triangles in actual diamonds are wave-based).

Remember: The purpose of "triangle identification" is just to tell you which triangles should be doing the call. Don't worry too much about the exact words the caller uses to do that. Once you have become familiar with the commonly-used terms, even if the caller combines them or has to make up a new one for some odd situation, the meaning should be pretty obvious. And once you have figured out whether you are in a triangle that should be doing the call, the words that were used to identify it don't affect how you actually do the call.